Question
The number of bacteria on a piece of toast triples every hour. If there is only one bacteria cell now, how many will there be in 24 hours? a. 1,062,882 b. 94,143,178,827 c. 16,106127 d.78.6432 What’s the answer from the answers I put
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GPT-4o mini
To determine the number of bacteria after 24 hours, given that the number triples every hour starting with 1 bacteria cell, we can use the formula:
\[ \text{Number of bacteria} = \text{initial amount} \times (\text{growth rate})^{\text{time}} \]
In this case:
- Initial amount = 1
- Growth rate = 3 (since it triples)
- Time = 24 hours
So the calculation becomes:
\[ \text{Number of bacteria} = 1 \times 3^{24} \]
Calculating \( 3^{24} \):
1. First, calculate \( 3^{24} \):
- \( 3^{24} = 3 \times 3 \times 3 \times \ldots \) (24 times)
Using an exponent calculator or calculating step by step, you can determine:
- \( 3^3 = 27 \)
- \( 3^6 = 729 \)
- \( 3^12 = 531441 \)
- \( 3^{24} = 282429536481 \)
This gives us a total of \( 282429536481 \) bacteria after 24 hours.
Now, looking at your options:
a. 1,062,882
b. 94,143,178,827
c. 16,106127
d. 78.6432
None of these options match the correct total of \( 282429536481 \). It looks like there may be an error in the options provided, as none correspond to the calculations based on the given growth rate.
\[ \text{Number of bacteria} = \text{initial amount} \times (\text{growth rate})^{\text{time}} \]
In this case:
- Initial amount = 1
- Growth rate = 3 (since it triples)
- Time = 24 hours
So the calculation becomes:
\[ \text{Number of bacteria} = 1 \times 3^{24} \]
Calculating \( 3^{24} \):
1. First, calculate \( 3^{24} \):
- \( 3^{24} = 3 \times 3 \times 3 \times \ldots \) (24 times)
Using an exponent calculator or calculating step by step, you can determine:
- \( 3^3 = 27 \)
- \( 3^6 = 729 \)
- \( 3^12 = 531441 \)
- \( 3^{24} = 282429536481 \)
This gives us a total of \( 282429536481 \) bacteria after 24 hours.
Now, looking at your options:
a. 1,062,882
b. 94,143,178,827
c. 16,106127
d. 78.6432
None of these options match the correct total of \( 282429536481 \). It looks like there may be an error in the options provided, as none correspond to the calculations based on the given growth rate.